American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

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London, December 30: American researchers claim to have solved a cryptic formula that renowned mathematician Srinivasa Ramanujan believed came to him in dreams while on his deathbed, the Daily Mail reported on Saturday.

The formula was contained in a letter he wrote to his mentor, the English mathematician G.H. Hardy, from his deathbed in 1920 outlining several new mathematical functions that had never been heard of before, together with a theory about how they worked. It had baffled mathematicians for more than 90 years, but new findings — presented at a conference at the University of Florida last month — reportedly show that Ramanujan's “hunch” about his formula was right — that it could explain the behaviour of black holes.

“We've solved the problems from his last mysterious letters,” said the well-known American mathematician Ken Ono of Emory University.

“For people who work in this area of math, the problem has been open for 90 years … Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died.”

He said the so-called “deathbed puzzle” which, according to Ramanujan, was revealed to him by the goddess Namagiri, may unlock secrets about black holes. “We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess. No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” said Professor Ono.

The Mail said that Ramanujan's letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

“Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value. Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1,” it said. Nobody at the time understood what the Indian mathematical genius was talking about.

“It wasn't until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Prof. Ono said.

His team, which used modern mathematical tools to solve the puzzle, was “stunned” to find the function could be used even today.

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News Network
April 18,2020

Washington, Apr 18: The United States on Friday passed 700,000 confirmed coronavirus cases, according to a tally maintained by Johns Hopkins University.

With the highest number of cases and deaths of any country in the world, the US had recorded 700,282 cases of COVID-19 and 36,773 deaths as of 8:30 pm (0030 GMT Friday), according to the Baltimore-based university.

That marked an increase of 3,856 deaths in the past 24 hours, but that figure likely includes "probable" virus-linked deaths, which had not previously been counted.

This week, New York City said it would add 3,778 "probable" virus deaths to its official count.

The US Centers for Disease Control and Prevention gave a toll Friday night of 33,049 dead, including 4,226 probable virus-linked deaths.

The United States has seen the highest death toll in the world in the coronavirus pandemic, ahead of Italy (22,745 deaths) although its population is just a fifth of that of the US.

Spain has recorded 19,478 deaths, followed by France with 18,681.

Trump announces $19 billion relief for farmers amid COVID-19 epidemic

President Donald Trump on Friday announced a $19 billion financial rescue package to help the agriculture industry weather the staggering economic downturn sparked by measures to defeat the coronavirus.

Trump told a press conference the government "will be implementing a $19 billion relief program for our great farmers and ranchers as they cope with the fallout of the global pandemic."

The program will include direct payments to farmers, ranchers and producers who Trump said have experienced "unprecedented losses during this pandemic."

Agriculture Secretary Sonny Perdue said US farmers have been hit hard by a sharp shift in demand, as schools and restaurants close and more Americans eat at home.

That has disrupted the food supply chain, forcing farmers in many places to destroy dairy output and plow under crops that no longer have buyers.

"Having to dump milk and plow under vegetables ready to market is not only financially distressing, but it's heartbreaking as well to those who produce them," Perdue said.

Perdue said some $3 billion of the money would go to buying produce and milk from such farmers, and redistribute it to community food banks.

Millions of Americans have recently turned to food pantries for meals and groceries after losing their jobs.

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News Network
April 26,2020

Washington/Seoul, Apr 26: A special train possibly belonging to North Korean leader Kim Jong Un was spotted this week at a resort town in the country, according to satellite images reviewed by a Washington-based North Korea monitoring project, amid conflicting reports about Mr. Kim's health and whereabouts.

The monitoring project, 38 North, said in its report on Saturday that the train was parked at the “leadership station” in Wonsan on April 21 and April 23. The station is reserved for the use of the Kim family, it said.

Though the group said it was probably Kim Jong Un's train, Reuters has not been able to confirm that independently, or whether he was in Wonsan.

“The train's presence does not prove the whereabouts of the North Korean leader or indicate anything about his health but it does lend weight to reports that Kim is staying at an elite area on the country's eastern coast,” the report said.

Speculation about Mr. Kim's health first arose due to his absence from the anniversary of the birthday of North Korea's founding father and Mr. Kim's grandfather, Kim Il Sung, on April 15.

North Korea's state media last reported on Mr. Kim's whereabouts when he presided over a meeting on April 11.

China has dispatched a team to North Korea including medical experts to advise on Kim Jong Un, according to three people familiar with the situation.

A third-generation hereditary leader who came to power after his father's death in 2011, Kim has no clear successor in a nuclear-armed country, which could present major international risk.

On Thursday, U.S. President Donald Trump downplayed reports that Mr. Kim was ill. “I think the report was incorrect,” Mr. Trump told reporters, but he declined to say if he had been in touch with North Korean officials.

Mr. Trump has met Mr. Kim three times in an attempt to persuade him to give up a nuclear weapons program that threatens the United States as well as its Asian neighbors. While talks have stalled, Mr. Trump has continued to hail Mr. Kim as a friend.

Reporting from inside North Korea is notoriously difficult because of tight controls on information.

A Trump administration official said continuing days of North Korean media silence on Mr. Kim's whereabouts had heightened concerns about his condition, and that information remained scant from a country U.S. intelligence has long regarded as a ”black box.”

The U.S. State Department did not immediately respond to questions about the situation on Saturday.

Daily NK, a Seoul-based website that reports on North Korea, cited one unnamed source in North Korea on Monday as saying that Kim had undergone medical treatment in the resort county of Hyangsan north of the capital Pyongyang.

It said that Mr. Kim was recovering after undergoing a cardiovascular procedure on April 12.

Since then, multiple South Korean media reports have cited unnamed sources this week saying that Mr. Kim might be staying in the Wonsan area.

On Friday, local news agency Newsis cited South Korean intelligence sources as reporting that a special train for Mr. Kim's use had been seen in Wonsan, while Mr. Kim's private plane remained in Pyongyang.

Newsis reported Mr. Kim may be sheltering from COVID-19, the respiratory disease caused by the novel coronavirus.

Mr. Kim, believed to be 36, has disappeared from coverage in North Korean state media before. In 2014, he vanished for more than a month and North Korean state TV later showed him walking with a limp.

Speculation about his health has been fanned by his heavy smoking, apparent weight gain since taking power and family history of cardiovascular problems.

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Agencies
July 8,2020

Washington D.C, Jul 8:  US Secretary of State, Mike Pompeo on Tuesday (local time) announced visa restrictions on some Chinese officials under the Reciprocal Access to Tibet Act, 2018.

"Today I am announcing visa restrictions on PRC government and Chinese Communist Party officials determined to be "substantially involved in the formulation or execution of policies related to access for foreigners to Tibetan areas," pursuant to the Reciprocal Access to Tibet Act of 2018," Pompeo said.

"Access to Tibetan areas is increasingly vital to regional stability, given the PRC's human rights abuses there, as well as Beijing's failure to prevent environmental degradation near the headwaters of Asia's major rivers," he said.

The US Secretary of State pointed out that Beijing has continued "systematically to obstruct travel to the Tibetan Autonomous Region (TAR) and other Tibetan areas" by U.S. diplomats and other officials, journalists, and tourists, while PRC officials and other citizens enjoy far greater access to the United States.

"The United States will continue to work to advance the sustainable economic development, environmental conservation, and humanitarian conditions of Tibetan communities within the People's Republic of China and abroad," he said.

Pompeo said US also remains "committed to supporting meaningful autonomy for Tibetans, respect for their fundamental and unalienable human rights, and the preservation of their unique religious, cultural, and linguistic identity".

"In the spirit of true reciprocity, we will work closely with the U.S. Congress to ensure U.S. citizens have full access to all areas of the People's Republic of China, including the TAR and other Tibetan areas," he said.

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